Absolutely not.
If you take out a loan for $94k, pay nothing up front, you pay the full length of the loan.
If you take out a loan for $100k, and pay $6k upfront (i.e. first payment) you reduce the length of your loan by several months.
Also, comparing month-to-month (looking at the amortization table), if you do the 2nd option, you will owe less money than if you do the former option. Not by a lot (anywhere from $50 to $6k, depending where on the loan you are), but that helps with being less upside down.
Assuming identical APR, and loan lengths